Nghiên cứu phương pháp thiết kế bộ điều khiển sử dụng ba đầu vào bằng logic mờ và đại số gia tử

Tuy nhien thuat toan thiSt ke bo dieu khien bang logic mcf va dai s6 gia i\i c6 dp phiic tap, thai gian tinh toan Ian han bg dieu khien PID se gay kho khan trong qua trinh thiet k6 cho c

NGHIEN CUtJ PHirONG PHAP THIET KE BO DIEU KHIEN SU^ DyNG BA DAU VAO B A N G LOGIC MOf VA D^I S6 GIA TU^

Nguyen H m i Cong^' *, Ng6 KiSn T r u n g \ Nguyin Tien Duy^

'Dai HQC Thai Nguyen, Phurnig Tan Thinh, Thanh pho Thai Nguyen

^Truong Dai hoc Ky thugt Cong nghiep, Dai hoc Thai Nguyen, Ditcmg 3-2,

Phuong Tich Lucmg, TP Thai Nguyen Email; conghn(S).tnu edu vn

Dan Toa soan: 23/I/20I4; CMp nhan dang: 26/3/2014

TOM TAT Trong nhung nam qua, vi?c nghien ciiu ling dung dai so gia tii trong ITnh vuc dieu khi6n da c6 nhung thanh cong dang ke Bg diSu khien su: dung dai s6 gia tu phat tri6n tu logic ma c6 thS ling dyng t6t cho cdc doi tuong cong nghi^p Tuy nhien thuat toan thiSt ke bo dieu khien bang

logic mcf va dai s6 gia i\i c6 dp phiic tap, thai gian tinh toan Ian han bg dieu khien PID se gay kho khan trong qua trinh thiet k6 cho cac d6i tugng yeu cau cao \k dg tac dong nhanh

Bai bdo trinh bay y tudng va thu|it toan thiet ke bg dieu khidn bang dai so gia tii vai viec

tang them dSu vao nhSm b6 sung lucmg thong tin \k su thay d6i trong h? thong cung nhir nhilu

tac dong, tir do giup ngiroi thiSt ke gian luge dugc s6 gia tri ngon ngu' va tap luat dieu khien, giam thilu khdi lirgmg tinh toan din den giam thM gian tinh toan cho vi xir li {bo di6u khi6n) dirge lira chgn thuc t8

Tie khoa: bg diSu khiSn su di^g dai s6 gia tii, b6 di6u khi6n ma, giam thai gian tinh todn

1 DAT VAN DE

Cac bg diSu khi^n thong minh ngay cang dugc un^ dung nhieu vao cac he thdng thyrc xk

trong cong nghiep Khi sir dung cac c6ng cu tinh toan mem nhu logic mo va dai so gia tu trong di8u khi6n c6 im diem: c6 th8 di6u khien dugc cac d6i tugng ma thong tin khong day du va n6u thi6t kg tot thi ban than cac bg dieu khiln nay la cac bg dieu khien thong minh nen kha phii hgp voi cac ddi tugng phi tuyen

Tuy nhiSn cac bg di^u khiln tren ciing t6n tai mgt so nhugc di8m:

(1) Dg phuc tap cua thu^t toan 16n, thai gian tinh toan Ion hem so vai bg di6u khi8n PID va d§n d6n khong th8 di8u khi6n dugc cac d6i tugng y8u cau cao ve dg tac dgng nhanh Vi vay, vSn

6k giam thai gian tinh toan va dan gian hoa trong ISp trinh vi xu li (bg dieu khien) ludn dugc cdc

(2) Voi y hiong la: n8u Idy diy du cac trang thai tron^ khong gian pha cua sai l$ch dua tai dau vao bg dieu khiSn (nhu bg d i k khiSn PID) thi se c6 thg giam dugc he luat va giam do phuc

tap tinh toan cua bg d i k khiln Tu y tuong do, cac tac gia da thik kk bg dieu khien ma vdi 3

dlu vao la sai lech, dao ham cua sai lech va tich phan cua sai lech va da dat dugc nhitng th^nh cong nhit dinh Kgt qua thu dugc la da giam dugc tuang d6i n h i k s6 luat di6u khi6n cho qua trinh thi8t k6 bg dieu khik Vi du nhu giam dugc tir 75 luat d i k khi8n xuong con 27 luat dieu khi6n trong [1] Tuy nhien, viec lam nay v3n t6n tai cac han che;

Viec ngi suy d6 tinh toan gia tn diu ra bg diSu khi6n la rit kho khan vi phai npi suy trong khong gian 4 chieu vai nhiSu phep tinh va cong thiic phuc tap

S6 lugng luat 6\hi khi6n con kha nhik, vi vay lap trinh khi thiSt kd bg digu khien vSn

con kha phuc tap

Theo tiSp can dai s6 gia tu, ta c6 thS kk nhap (co trong so) cac gia tti dinh lugng ngu nghia

cua cac biSn vao (anh xa: R^->R) dl xac dinh dugc m6i quan he vao - ra trong kh6ng gian 2

chieu va c6 th^ gian luge s6 lugng luat dik\i khien kha nhilu so v6i dieu khien raa Tren ca so phan tich tren, bai bao nghien cuu phuong phap thiSt k& bg dieu khien ma vai 3 dau vao, tir do

ap dung vai bg dilu khiSn sijr dung dai so gia tu va so sanh danh gia k6t qua dat dugc bang m6 phong tren doi tugng phi tuyen cu the

B6 sung diu vao thu ba dong thai gian luge s6 luat diSu khien a day la mot bai toan mo'i voi li thuyet dai so gia tir Viec bo sung nay nham cung cap them thong tin dau vao cho

bg di6u khien dong thai khong dugc lam tang tinh phi myen va phuc tap hoa qua trinh thiet ke Vcri myc tieu dieu khien he thong bam theo tin hieu vao, bai bao da chgn dau vao thii 3 la tich phan cua sai lech nh5m khu sai lech tmh, dam bao do chinh xac cho he thdng

Viec tang them dau vao thu ba se bo sung lugng thong tin ve sir thay doi trong he thong cung nhu nhieu tac dgng, tir do giup nguai thiet ke gian luge dugc so gia tri ngon ngii va tSp lu5t di6u khien, giam thiSu kh6i lugng tinh toan din d6n giam thdi gian tinh toan cho

vi xu li (bg dieu khien) dugc lira chgn thgc te

2 THIET KE BQ DIEU KHIEN SU" DUNG DAI SO GIA TU" VOI 3 DAU VAO Nhom tac gia tiSn hanh nghien cim va so sanh phuong phap thi6t k8 bp diSu khiln sir dung

3 dau vao bang dai so gia hi va logic ma vai cimg mot thuat toan thi6t kL Cac k6t qua d i k

khien va hieu qua thuc hien dugc the hien qua bai toan dieu khien mot doi tugng phi tuyen trong

thuc t%

2.1 Fhinrag phap thiet ke bp dieu khiSn su- dung d^i s6 gia tur

2.1.1 Giaithieu torn tat dai so gia tie

Dai so gia tu (Hedge Algebra - HA) la su phat triSn di^a tren tu duy logic \h ngon ngft [3],

[4] Vai quan he vao - ra theo logic ma phai xac dinh cac ham lien thupc mot each roi rac thi voi

HA CO mot cdu true d^i s6 duoi dang quan he ham, cho phep hinh thanh mot tSp gia tri ng6n ngii Ian vo han sao cho cau true thu dugc mo phong tot ngu nghTa ciia ngon ngir giup cho cac qua

Chang han, khi xet mot tap gia tri ngon ngii la m i k ciia biSn ngon ngu cua bidn chan li TEMPERATURE g6m cac tir sau:

T =- dom(TEMPERATURE) = {Large, Small, very Large, very Small, more Large, more

Small, approximately Large, approximately Small, little Large, little Small, less Large, less Small, very more Large, very more Small, very possible Large, very possible Small, }

Khi do mien ngon ngir T = dom(TEMPERATURE) c6 thS biSu thi nhu la mot cku tnic dai

s6 AT = (T, G, H, <), trong do: T la tap n6n ciia AT; G la tap cac tir nguyen thuy (tap cac phan

tu sinh: Large, Small); H la tap cac toan tu mot ngoi, ggi la cac gia tii (cac trang tir nhdn); < la bi€u thi quan h6 thii tu tr8n cac tii (cac khai niem ma), no dugc "cam sinh" tii ngCi nghia tu nhien <cua cac tii> Vi du: dira tren ngiir nghia, cac quan he thii tu sau la dung: Small<Large, more Large<very Large, very Small < more Small, possible Small < Large, Small < possible Small,

2.1.2 Bo dieu khien siedungHA

Bg didu khien HAC (Hedge Algebra based Controller) g6m 3 khdi nhu Hinh 1

Normalization

&SQMS

(I)

Quantified Rule Base &

HA-lRMd (H)

Denormalization

(III)

HA Controller

Hinh I S c do bg dieu khien HAC

Trong do: x gia tri dat dau vao; Xj gia tri ngii nghia dau vao; « gia tri diiu khidn va «j gia tri

ngii nghia dieu khien Bp HAC gom cac kh6i sau:

Khdi I - Ngii nghia hoa (Normalization & SQMs): bien ddi tuydn tinh x sang Xj

Khdi II - Suy luan ngii nghia va he luat ngu nghia (Quantified Rule Base & HA-IRMd): thuc hi$n phep ngi suy ngu nghia tir Xj sang Uj tren ca sd anh x^ ngii nghia dinh lugng

vk didu kien he luat

KJhdi III - ChuSn hoa dau ra (Denormalization): b i k ddi tuyen tinh u^ sang u

2.2 Bg d i k khiin sfr dijng dai so gia tu- 3 dau vao - NEWHAC

Tac gid trong [1] da thi8t ke bg dieu khien md vdi 3 dau vao la sai lech, dao ham sai lech, tich phan ciia sai lech va da dat dugc nhung thanh cong nhat dinh vdi ket qua la da giam dugc tii

75 luat didu khien xudng con 27 luat dieu khien Tuy nhien, viec ngi suy dd tinh toan gia tri dSu

ra bg dieu khien la rat kho khan vi phai npi suy trong khong gian 4 chieu vai nhieu phep tinh va cong thiic phiic tap Viec giam xudng con 27 luat dieu khien da tot han nhieu so vdi he luat ban dSu nhung so lugng luat difiu khiSn nhu vay van con kha nhieu va kha phiic tap khi lap trinh thiSt ke bp dieu khien

Ke thira bai toan tren ciia dieu khien md theo tiep can HA, ta cd the kdt nhap (cd trong sd) cac gia tri dinh lugng ngu' nghta cua cac bidn vao (anh xa: R^^R) de xac dinh dugc mdi quan h?

vao - ra trong khdng gian 2 chiSu nen cd thg tidp tuc gian luge them dugc kha nhieu so lugng luat dieu khien

Kit qua DghiSn cihi cua [1]

Da tidk kB bg di6u khiln md gom 3 dku vao: diu vac sai Idch e(t), ki hieu E vdi 5 bien ngon ngO; dau vao dao ham sai lech de(l), ki hieu DE vdi 5 bidn ngon ngii va dSu vao tich phan sai lech left) ki hieu IE vdi 3 bi6n ngon ngu

Da gian luge tti 75 tap luat dieu khiSn con 27 tap luat didu khidn cho bg dieu khien md nha thuc nghiem vdi y kiSn chuyen gia

ThuSt toan thiet kl bS di^u khien su dyng HA 3 dSu vao - NEW_HAC

Bu&c T

Chpn bg tham sd vdi 3 dku vao gdm diiu vao sai lech e(t), ki hieu E vdi 5 bien ngon ngii; dJiu vao dao ham sai lech de(t), ki hieu DE vdi 5 bidn ngon ngft va d§u vao tich phdn sai lech ie(t) ki hieu IE vdi 3 biSn ngdn ngir DSu ra la dien ap mot chidu ki hieu U vdi 5

bien ngon ngu

Tinh toan cac gia tri dinh lugng ngii nghia cho E, DE, IE, U

Buac 2: Cai tien h? luat

Thanh lap bang SAM tir 27 lu^t di6u khi6n [1] vdi cac gia tri dinh lugng ngii nghia da tinh cho E, DE, IE va U

D6 tranh mSt mat thdng tin so vdi viec su dung phep ket nhSp "min ", sii dyng phep ket

nhap cd trpng sd cac gia tri dau vao vdi:

Input_NEW_HAC = w,*E-l-W2*DE-l- W3*IE

theo Output_ NEW_HAC = U

Liic nay, dau vao Input_ NEW_HAC gdm 27 gia tri dinh lugng ngu: nghia va dau ra bd dieu khien Output_ NEW_HAC gdm 5 gia tri dinh lugng ngii nghia Ket nhap 27 diem dinh lugng ngir nghia nay bang phep lay trung binh cac diem cd cung gia trj dau ra (Output_ NEW_HAC) Tap luat dieu khien se giam xudng chi con 5 luat diSu khiSn

Qua khao sat thay rang vdi phep kSt nhap nay lugng thong tin bi mat mat la it nhk,

khdng lam tang do phitc tap cua dudng cong ngir nghia ma lai cho k6t qua chinh xac nhat

De dam bao he thdng vin trong mien xac dinh, lay them 2 luSt tai hai diu mi8n vdi gia tri la 0 va 1 Vay bg NEW_HAC cai tien dugc thiet k6 gdm 3 dau vao va 7 tap luat di6u khien

Buac 3

Xay dung dudng cong ngir nghia

Giai dinh lugng ngii nghia tim gia tri thuc

3 LTNG DUNG BO NEW_HAC CHO HE THONG PHI TUYEN BALL AND BEAM

Hinh 2 Mo ta he th6ng Ball and Beam [2]

He thdng Bail and Beam duac sir dung rpng rai, dugc md ta trong Hinh 2, nhiem vu ciia

dieu khien la giii cho Ball d vi tri mong mudn Vi tii ciia Ball dugc do bdi cam biln, Ball Ian dpc

tren chieu dai ciia Beam, Beam dugc truyen dong qua true dgng co dien nen cd the nghieng xung

quanh trgng tam thdng qua tin hieu di6u khien dgng ca Cong viec dieu khiln la dieu chinh mpt

each tir dgng vi tri cua Ball tren Beam bang viec thay ddi gdc cua Beam vi Ball gia tdc ty le vdi

do nghieng cua Beam Day la nhiem vu dieu khien kho idian bdi vi Ball khdng diing yen tren

mot vi tri cd dinh tren Beam Trong thuc t6 Ball and Beam cd cac thanh phan dong bdi dong co,

cac nhieu lam anh hudng den each dieu khien Xay dung dugc md hinh phi tuyen cho he Ball

and Beam hi cac cdng thiic (1), (2), (3)

'x = —gsma (1)

a = -e (2)

^(^)',(,,i,^^)

3.2 Thi^t ke bO NEW_HAC 3 dSu viko

Buac 1:

Chgn bg tham sd tinh toan:

G = {Negative (N), Positive (P};

i r = { Little (L)}; H^={Very(V)};

Nhan ngdn ngii trong HA cho cac bien dau vao, ra nhu sau:

BiSn ngdn ngft E, DE, U:

Very Negative (VN)

Little Negative (LN)

Little Positive (LP)

Very Positive (VP)

Bien ngon ngii dau vao tiitr ba IE:

Negative (N)

Positive (P)

Theo [1], ta CO 27 luat diSu khi6n tuong duong cho cac nhan ngon ngO HA nhu Bang 1

Bang 1 27 luat dieu khien

E = W

DE = W U = LP

IE = P

E = W

DE = W U = LN

I E = N

IE = W

E

U

VN

LN

W

LP

VP

VN

VN

VN

VN

LN

W

LN

VN

VN

LN

W

LP

W

VN

LN

W

LP

VP

LP

LN

W

LP

VP

VP

VP

W

LP

VP

VP

VP Tinh toan cac gia tri dinh lugng ngii nghia cho E, DE, IE va U

Buac 2

Thanh lap bang SAM tir bang 1 vdi cac gia tri dinh lugng ngii nghia da tinh cho E, DE,

IE va U dupe Bang 2

Bang 2 Bang SAM g6m 27 luat

[E = 0,675

E = 0,5

DE = 0,5

[E = 0,325

E = 0,5

DE = 0,5

IE=0,5

E

U=0,625

U=0,375

U 0,1513

0,3988

0,5 0,6012 0,8488

DE

0,1513 0,125 0,125 0,125 0,375 0,5

0,3988 0,125 0,125 0,375 0,5 0,625

0,5 0,125 0,375 0,5 0.625 0,875

0,6012 0,375 0,5 0,625 0,875 0,875

0,8488 0,5 0,625 0,875 0,875 0,875 Lira chgn cac trgng so ket nhap theo kinh nghiem, sir dung phep kdt nhap cd trgng sd k6t nhap cac dau vao hiput_NEW_HAC=W|*E+W2*DE+ W3*IE theo U ta cd bang SAM2

Bang 3 Bang SAM2 gom 27 luat

Rule

1

2

3

4

5

6

7

8

9

10

11

12

13

Input_

NEW_HAC 0,225735

•0,328065 0,35565 0,383235 0,48561 0,339435 0,441765 0,46935 0,496935 0,59931 0,370085 0,472415 0,5

Output NEWHAC 0,125 0,125 0,125 0,375 0,5 0,125 0,125 0,375 0,5 0,625 0,125 0,375 0,5

14

15

16

17

18

19

20

21

22

23

24

25

26

27

0,527585 0,62996 0,400735 0,503065 0,53065 0,558235 0,66061 0,514485 0,616815 0,6444 0,671985 0,77436 0,50875 0,49125

0,625 0,875 0,375 0,5 0,625 0,875 0,875 0,5 0,625 0,875 0,875 0,875 0,625 0,375

Su dung phep tinh trung binh cho cac gia tri dinh lugng ngir nghia ciia bien vao trong bang 3 tren tuong ling bien ra theo cdng thirc:

( J ] Input _ NEW _HAC,)ln

vdi n la sd luat cd cung dlu ra OutputNEWHAC (U) Liic nay cdn 5 gia in dinh lugng Input^NEWHAC tuang ling vdi 5 gia tri dinh lugng Output_ NEW_HAC (U) Bd sung them 2 phSn tii trong HA mang y nghia "myet ddi" vdi gia tri la 0 va 1 ta dugc bang SAM3 nhu Bang 4 gdm 7 luat

Bang 4 Bang SAMS gom 7 luat

Rule

28

1,2,3,6,7,11

4,8,12,16,27

5,9,13,17,21

10,14,18,22,26

15,19,20,23,24,25

Input_NEW_HAC

0 0,343455833 0,443397 0,5 0,556622 0,656591667

O u t p u t N E W H A C

0 0,125 0,375 0,5 0,625 0,875

Buac 3

Dudng cong ngu nghia dinh lugng bieu dien mdi quan he vao - ra the hien tren Hinh 3

Hinh 3 Dudng cong ngu: nghia dinh lugng bilu diln m6i quan he vao - ra

3.3 Ket qua mo phong

3.3.1 So sanh ket qua vai bo dieu khien HAC 2 ddu vao

Thiet ke bd HAC 2 dSu vao gdm sai lech va dao ham sai lech

Md phdng tren Matlab - Simulink bp HAC 2 dku vao va 3 dau vao vdi so dd md phong

nhu Hinh 4 va ket qua nhu Hinh 5

Hinh 4 Mo phong he vdi 2 bg HAC

HAC2tJPUT-N£WH

./*>«.4,.>,,.w •vfm ^HV4-^,.fr•^,fi<ij',,^^^^n4»|

Hinh 5 Dap ung he thong vdi 2 bg HAC

Nh^n xet

Vdi h | thong phi tuySn Ball and Beam la mot he thdng chiu nhigu anh hudng cua nhiiu,

da thi^t ke 2 bd dieu khidn HAC 2 dlu vao va 3 dau vao Kit md phdng nhan thSy ca hai

bd dieu khien dap irng nhanh, thdi gian qua dp nhd va chiu dugc su tac dong ciia nhilu Ket qua md phdng cho thay bg dieu khidn HAC vdi 3 dau vao dap ling nhanh va vln dam bao chat lugng, dieu nay chiing td tinh diing dan ciia phuong phap thiet kS bang vigc bd sung them thdng tin cho he thdng khi cd them dau vao va tinh chinh xac ciia phep ket nhap

3.3.2 So sanh ket qua vai bo dieu khien FLC 3 dau vao

Theo k6t qua cua tai lieu [1] chi giam dugc tir 75 luat di6u khidn xudng cdn 27 tap luat dieu khien md Mudn gian luge them sd luat dieu khien cua bg dieu khien md tii 27 luat nay thi lai phai qua thuc nghiem nhieu Ian vdi y kien chuyen gia

Vdi phuong phap thi6t kS bd NEW_HAC 3 diiu vao da giam xudng cdn 7 luat dieu Ichien tu 27 t|p luat md Vdi y tudng mong mudn tiep tuc gian luge sd luat dieu khien cho bg dieu khien md tir 27 luat dieu khien xudng cdn 7 luat dieu khien vdi cung thuat toan thiet k6 tuang duong (bd NEW_HAC 3 dau vao) de kiem tra tinh diing dan ciia thuat toan Tir 7 tap luat cua bd dilu khien NEW HAC 3 dau vao, ddi chieu so sanh anh

xa dugc 7 luat md tuang duong tir 27 tap luat dieu khien md Thiet k8 bd didu khi6n md

3 dau vao vdi 7 tap luat dieu khien tuang duang 7 luat ciia bp HAC 3 diu vao:

If E - LN and DE = VN and IE = W then U = VN (Rule 6)

If E = LN and DE = W and IE = W then U = LN (Rule 8)

If E = LP and DE = LN and IE - W then U = W (Rule 17)

If E = LP and DE = W and IE = W then U = LP (Rule 18)

If E = LP and DE = VP and IE = W then U - VP (Rule 20)

If E = W and DE = W and IE = N then U = LN (Rule 27)

Md phdng bd FLC va NEWHAC 3 dau vao vdi ciing thuat toan thiet ke va he luat dieu khien cd so do md phdng nhu hinh 6 va ket qua nhu Hinh 7

K)f

Hinh 6 Mo phong he thong vdi bg FLC va NEW_HAC

HAC 3 INPUT-FLC 3 INPUT

' S -iK ' 4

- / ''•''^r'v^.ii'Af\f:'M^^':ii<i- iit:, -:Ax.- ~ \, i

1 2 3

Hinh 7 Ket qua vai b5 FLC va NEW_HAC

Ket qua mo phong cho thay, neu cung giam xu6ng 27 tap luat thi chdt lugng bo FLC va

bg NEW_HAC la nhu nhau Tuy nhien, n6u giam xu6ng con 7 tap luat thi bg NEW^HAC van dam bao chit lugng trong khi bg FLC voi 7 tap luat (anh xa tir 7 tap luat dieu khien cua NEW EIAC) Ithong the dieu Idiien dugc

Phuong phap sit dung HA voi viec tang dau vao va giam s6 lugng luat la huong dung dan, cho ta ket qua tot trong khi cung v6i cimg mot thuat toan thiet kS thi bg dieu k h i k